For coherent demodulation of modulated signals, a transmitted carrier frequency and phase must be recovered at the receiver in order to demodulate a modulated signal. If a dominant carrier spectral line exists in the modulated signal, a simple bandpass filter followed by a phase-locked loop (PLL) may be used to recover the transmitted carrier frequency and phase from the modulated signal. In modern communication systems, a carrier signal is often suppressed to save power. When the carrier signal is suppressed, more advanced methods must be utilized to recover the transmitted carrier frequency and phase of a modulated signal.
For communication systems with suppressed carriers, blind carrier recovery methods, such as Costas loop, Viterbi and Viterbi, and decision directed methods, use signal constellation properties at baseband to estimate and correct frequency offset between the transmit carrier and the carrier generated locally at the receiver, such as by the use of an oscillator. The use of signal constellation properties at baseband, as in the above mentioned known blind carrier recovery methods, leads to lower jitter and requires lower implementation cost in comparison to carrier recovery methods that work with the carrier signal directly. Due to inherent phase ambiguity of the signal constellation, the known blind carrier recovery methods often have a limited capture range smaller than
            2      ⁢                          ⁢      π        M    ,where M is the signal constellation size. This precludes the use of known blind carrier recovery methods when the frequency offset between transmit carrier and receive carrier is larger than
            2      ⁢                          ⁢      π        M    .
In communication systems, such as optical and wireless communication systems, the locally generated carrier frequency at the receiver may differ from the carrier frequency at the transmitter. The offset of the carrier frequency (hereinafter referred to as the carrier frequency offset) may be as large as the signal bandwidth of the modulated signal. For example, commercial tunable laser oscillators have an accuracy of ±2.5 GHz which leads to a carrier frequency offset as large as 5 GHz.
There often exists a tradeoff between capture range and accuracy for constellation-based blind carrier recovery schemes: the larger the desired captured range, the coarser the frequency estimation accuracy. Even when the frequency offset is less than
            2      ⁢                          ⁢      π        M    ,it is beneficial to have a simple coarse carrier recovery scheme to first correct some carrier frequency offset before a signal constellation-based carrier recovery scheme is applied.
For spectrally flat channels, such as fiber channels or certain wireless channels, a carrier frequency offset may be estimated by finding the center of the spectrum of the oversampled baseband signal. The spectrum of the oversampled baseband signal may be implemented by fast Fourier transform (FFT). The accuracy of this method is determined by the FFT size and the number of FFT blocks. Drawbacks of this method of estimating the carrier frequency offset include its relatively high complexity and coarse accuracy.
A method for blindly estimating and correcting a carrier frequency offset at a receiver is described in U.S. Patent Application Publication No. 2011/0085797. The method described in this patent publication exploits the relationship between a frequency offset and a maximal phase error measured with the known Gardner algorithm for timing offsets within one symbol duration. This requires the evaluation of Gardner phase errors at a number of timing offsets, typically in the order of a dozen to a few tens of timing offset values. To do so, the received digital signal also needs to be digitally up-sampled to a higher rate. The accuracy of this coarse frequency offset estimation is in the range of ±1 GHz, which is still large for the fine signal-based carrier recovery methods and limits its application to small signal constellations. A drawback of the method disclosed in this patent is that it utilizes a complicated digital up-sampler to oversample the received signal that is originally sampled at no more than two samples per symbol.
Improvements in methods for estimating and correcting carrier frequency offsets are therefore desirable.